304 BELL SYSTEM TECHNICAL JOURNAL 



The most important of these differences in classes is that arising 

 from the reciprocity theorem. Of the three classes, only the T 

 (open-circuit and short-circuit transfer impedances) includes members 

 which are equal by the reciprocity theorem; this follows because the 

 reciprocity theorem requires interchange of voltmeter (or ammeter) 

 and source with associated ammeter (or voltmeter) and the T class 

 alone permits this. It is a matter of taste whether such duplicates 

 should be counted separately or as one ; in the interest of keeping large 

 figures as low as possible they are here counted as one, since the 

 classification is such that the other alternative may be taken merely 

 by doubling the r„. 



Another reason for keeping the T class distinct is that total open- 

 circuit and short-circuit transfer impedances for a given number of 

 terminals are equal in number. This is proved immediately by 

 observing that the two connections shown in Fig. 2 for this class are 

 in one-one correspondence: each may be obtained from the other by 

 interchanging voltmeter and ammeter. Moreover, if T°x, n and T\, n 

 are the numbers of open-circuit and short-circuit transfer impedances 

 measurable when short circuits have been placed across the n terminals 

 in all possible ways so as to realize x terminals, each merged group of 

 terminals counting as a single terminal, the correspondence leads to 

 the relation 



since the interchange of voltmeter and ammeter in the measuring 

 arrangement for open-circuit transfer impedances results in one less 

 available terminal, two terminals being merged by the ammeter short 

 circuit. Note that T^i, „ = T\, „ = 0, since with just two terminals, 

 no non-source voltages and with n terminals no non-source currents 

 are measurable. 



Equation (I) is important in determining enumerating expressions 

 in the section following. 



Enumerating Expressions 



The laws of enumeration appear most simply exposed by examining 

 the simplest cases first. 



For two terminals, there is but one measurable impedance, the 

 driving-point impedance between the terminals. 



For three terminals, with the terminals distinct, there are three 

 driving-point and three open-circuit transfer impedances, for there are 

 three ways of selecting driving pairs of the three terminals and for 

 each selection two ways of selecting pairs for open-circuit voltage 



